diff --git a/lib/rubocop/cop/rspec/stubbed_mock.rb b/lib/rubocop/cop/rspec/stubbed_mock.rb
index 0b7d0a0a7..10a8198f5 100644
--- a/lib/rubocop/cop/rspec/stubbed_mock.rb
+++ b/lib/rubocop/cop/rspec/stubbed_mock.rb
@@ -16,6 +16,13 @@ module RSpec
       class StubbedMock < Base
         MSG = 'Prefer `%<replacement>s` over `%<method_name>s` when ' \
               'configuring a response.'
+        REPLACEMENTS = {
+          expect: :allow,
+          is_expected: 'allow(subject)',
+          expect_any_instance_of: :allow_any_instance_of
+        }.freeze
+        REPLACABLE_METHODS = Set.new(REPLACEMENTS.keys).freeze
+        RESTRICT_ON_SEND = %i[to].freeze
 
         # @!method message_expectation?(node)
         #   Match message expectation matcher
@@ -60,7 +67,7 @@ class StubbedMock < Base
         #   @yield [RuboCop::AST::Node] expectation, method name, matcher
         def_node_matcher :expectation, <<~PATTERN
           (send
-            $(send nil? $#Expectations.all ...)
+            $(send nil? $REPLACABLE_METHODS ...)
             :to $_)
         PATTERN
 
@@ -133,8 +140,6 @@ class StubbedMock < Base
           }
         PATTERN
 
-        RESTRICT_ON_SEND = %i[to].freeze
-
         def on_send(node)
           expectation(node) do |expectation, method_name, matcher|
             on_expectation(expectation, method_name, matcher)
@@ -157,18 +162,7 @@ def on_expectation(expectation, method_name, matcher)
         def msg(method_name)
           format(MSG,
                  method_name: method_name,
-                 replacement: replacement(method_name))
-        end
-
-        def replacement(method_name)
-          case method_name
-          when :expect
-            :allow
-          when :is_expected
-            'allow(subject)'
-          when :expect_any_instance_of
-            :allow_any_instance_of
-          end
+                 replacement: REPLACEMENTS.fetch(method_name))
         end
       end
     end
diff --git a/spec/rubocop/cop/rspec/stubbed_mock_spec.rb b/spec/rubocop/cop/rspec/stubbed_mock_spec.rb
index 37ee2e686..2ad0be1e1 100644
--- a/spec/rubocop/cop/rspec/stubbed_mock_spec.rb
+++ b/spec/rubocop/cop/rspec/stubbed_mock_spec.rb
@@ -126,7 +126,7 @@
     RUBY
   end
 
-  it 'tolerates passed arguments without parentheses' do
+  it 'flags even when passed arguments without parentheses' do
     expect_offense(<<~RUBY)
       expect(Foo)
       ^^^^^^^^^^^ Prefer `allow` over `expect` when configuring a response.
@@ -134,4 +134,39 @@
         .with(bar).and_return baz
     RUBY
   end
+
+  it 'flags `should_receive`', skip: 'Not implemented yet' do
+    expect_offense(<<~RUBY)
+      foo.should_receive(:bar).and_return(:baz)
+      ^^^^^^^^^^^^^^^^^^^ Prefer `allow` over `should_receive` when configuring a response.
+    RUBY
+  end
+
+  it 'flags `should_not_receive`', skip: 'Not implemented yet' do
+    expect_offense(<<~RUBY)
+      foo.should_not_receive(:bar)
+      ^^^^^^^^^^^^^^^^^^^^^^ Prefer `allow(...).not_to receive` over `should_not_receive` when configuring a response.
+    RUBY
+  end
+
+  it 'flags `are_expected`', skip: 'Not implemented yet' do
+    expect_offense(<<~RUBY)
+      are_expected.to receive(:bar).and_return(:baz)
+      ^^^^^^^^^^^^ Prefer `` over `are_expected` when configuring a response.
+    RUBY
+  end
+
+  it 'flags `should`', skip: 'Not implemented yet' do
+    expect_offense(<<~RUBY)
+      foo.should receive(:bar).and_return(:baz)
+      ^^^ Prefer `allow` over `should` when configuring a response.
+    RUBY
+  end
+
+  it 'flags `should_not`', skip: 'Not implemented yet' do
+    expect_offense(<<~RUBY)
+      foo.should_not receive(:bar)
+      ^^^^^^^^^^ Prefer `allow(...).not_to receive` over `should_not` when configuring a response.
+    RUBY
+  end
 end